Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone

Abstract

Trabecular plates and rods are important microarchitectural features in determining mechanical properties of trabecular bone. A complete volumetric decomposition of individual trabecular plates and rods was used to assess the orientation and morphology of 71 human trabecular bone samples. The ITS-based morphological analyses better characterize microarchitecture and help predict anisotropic mechanical properties of trabecular bone.

Introduction: Standard morphological analyses of trabecular architecture lack explicit segmentations of individual trabecular plates and rods. In this study, a complete volumetric decomposition technique was developed to segment trabecular bone microstructure into individual plates and rods. Contributions of trabecular type-associated morphological parameters to the anisotropic elastic moduli of trabecular bone were studied.

Materials and methods: Seventy-one human trabecular bone samples from the femoral neck (FN), tibia, and vertebral body (VB) were imaged using muCT or serial milling. Complete volumetric decomposition was applied to segment trabecular bone microstructure into individual plates and rods. The orientation of each individual trabecula was determined, and the axial bone volume fractions (aBV/TV), axially aligned bone volume fraction along each orthotropic axis, were correlated with the elastic moduli. The microstructural type-associated morphological parameters were derived and compared with standard morphological parameters. Their contributions to the anisotropic elastic moduli, calculated by finite element analysis (FEA), were evaluated and compared.

Results: The distribution of trabecular orientation suggested that longitudinal plates and transverse rods dominate at all three anatomic sites. aBV/TV along each axis, in general, showed a better correlation with the axial elastic modulus (r(2) = 0.95 approximately 0.99) compared with BV/TV (r(2) = 0.93 approximately 0.94). The plate-associated morphological parameters generally showed higher correlations with the corresponding standard morphological parameters than the rod-associated parameters. Multiple linear regression models of six elastic moduli with individual trabeculae segmentation (ITS)-based morphological parameters (adjusted r(2) = 0.95 approximately 0.98) performed equally well as those with standard morphological parameters (adjusted r(2) = 0.94 approximately 0.97) but revealed specific contributions from individual trabecular plates or rods.

Conclusions: The ITS-based morphological analyses provide a better characterization of the morphology and trabecular orientation of trabecular bone. The axial loading of trabecular bone is mainly sustained by the axially aligned trabecular bone volume. Results suggest that trabecular plates dominate the overall elastic properties of trabecular bone.

FIG. 1

Results of the complete volumetric decomposition procedure on image of vertebral trabecular bone sample (3.2 × 3.2 × 2.1 mm³). (A) An original image of a trabecular bone sample. (B) Results of skeletonization and topological classification of A. Inner surface voxels are shown as red, surface edge voxels in green, inner curve voxels in light blue, curve end voxels in pink, R-R junctions in orange, and P-R junctions in yellow. (C) Results of arc-skeletonization and topological classification of B. Arc voxels are shown as red, inner curve voxels in light blue, curve end voxels in pink, P-P junctions in dark blue, R-R junctions in orange, and P-R junctions in yellow. (D) Results of the decomposition of C. (E) Intermediate result of reconstruction to B. (F) Result of complete reconstruction to A. Colors indicate different branches in D–F.

FIG. 2

Illustrations of complete volumetric decomposition on images of trabecular bone samples (2.1 × 2.1 × 1.3 mm³) from different anatomic sites: FN (A), tibia (B), and VB (C). (Left) Trabecular bone structures with the trabecular type labeled for each voxel. Plate voxels are shown in red, rod voxels in green. (Right) Completely decomposed trabecular bone structures with individual trabeculae labeled by color for each voxel. (A) 119 plates and 51 rods. (B) 72 plates and 46 rods. (C) 50 plates and 42 rods.

FIG. 3

(Top) Illustration of transformation of imaging coordinate of axes x, y, and z to a new coordinate system of orthotropic axes: X₁, X₂, and X₃. (Bottom) Definition of Φ₃ for trabecular plates and rods.

FIG. 4

(A–C) Histograms of orientations of trabecular plate (left) and rod (right) along X₃-axis within different anatomical sites: FN (A), tibia (B), and VB (C).

FIG. 5

Histograms of trabecular plate and rod thickness within different anatomical sites: FN (A), tibia (B), and VB (C).

FIG. 6

Results of correlation analyses between axial elastic modulus E_ii and bone volume fraction (BV/TV), plate bone volume fraction (pBV/TV), and X_i axial bone volume fraction (aBV/TV)_i by nonlinear regression of power laws (i = 1, 2, and 3). p < 0.001 for all the correlations.